Index: wp-includes/pluggable.php
===================================================================
--- wp-includes/pluggable.php	(revision 17786)
+++ wp-includes/pluggable.php	(working copy)
@@ -401,6 +401,14 @@
 
 	foreach ( (array) $to as $recipient ) {
 		try {
+			// Break $recipient into name and address parts if in the format "Foo <bar@baz.com>"
+			$recipient_name = '';
+			if( preg_match( '/(.+)\s?<(.+)>/', $recipient, $matches ) ) {
+				if ( count( $matches ) == 3 ) {
+					$recipient_name = $matches[1];
+					$recipient = $matches[2];
+				}
+			}
 			$phpmailer->AddAddress( trim( $recipient ) );
 		} catch ( phpmailerException $e ) {
 			continue;